Monostable Stochastic Resonance Research Articles

Fault diagnosis of rolling bearing based on the three-dimensional coupled periodic potential-induced stochastic resonance

Abstract Conventional bistable and monostable stochastic resonance (SR) methods exhibit certain limitations in their capacity to enhance and extract incipient characteristics. Firstly, the inherent potential function structure, characterized by a singular stable-state paradigm, proves inadequate in accommodating the heterogeneous and multifaceted condition monitoring signals. Secondly, the interconnected dynamic characteristics of the mechanical signals remain unaccounted for. Furthermore, conventional SR methods persist in utilizing a fixed constant as the critical system parameter, thereby neglecting the synergistic interaction among monitoring signals, potential function structures, and scale factors. Owing to the rich dynamic characteristics of the three-dimensional multi-stable coupled periodic potential SR system, it demonstrates superior noise utilization compared to monostable and bistable systems. In view of this, the present formulates a three-dimensional spatial model employing a coupled periodic potential model with nonlinear coupling. Subsequently, a pioneering method for diagnosing rolling bearing faults is introduced, utilizing the framework of three-dimensional multi-stable coupled periodic potential-induced SR. Simulation and experimental results illustrate that this approach effectively enhances and extracts the subtle fault characteristics of rolling bearings, ensuring a clear distinction between the spectral peak at the bearing fault characteristic frequency and the spectral peak originating from the interference noise.

Monostable stochastic resonance activation unit-based physical reservoir computing

Monostable stochastic resonance activation unit-based physical reservoir computing

Automatic Extraction Method of Weld Weak Defect Features for Ultra-High Voltage Equipment

To solve the problems of low precision of weak feature extraction, heavy reliance on labor and low efficiency of weak feature extraction in X-ray weld detection image of ultra-high voltage (UHV) equipment key parts, an automatic feature extraction algorithm is proposed. Firstly, the original weld image is denoised while retaining the characteristic information of weak defects by the proposed monostable stochastic resonance method. Then, binarization is achieved by combining Laplacian edge detection and Otsu threshold segmentation. Finally, the automatic identification of weld defect area is realized based on the sequential traversal of binary tree. Several characteristic analysis dimensions are established for weld defects of UHV key parts, including defect area, perimeter, slenderness ratio, duty cycle, etc. The experiment using the weld detection image of the actual production site shows that the proposed method can effectively extract the weak feature information of weld defects and further provide reference for decision-making.

Research on the Weak Signal Extraction Method with Adaptive Stochastic Resonance Based on the Time Grid Sensor for PMSM

Because the output signal of the time grid sensor is so weak and is easily affected by the disturbing noise, it is difficult to extract the induction signal containing the position information, when the time grid sensor is used to detect the rotor position of the permanent magnet synchronous motor (PMSM). In this paper, an adaptive monostable stochastic resonance method is proposed to realize the weak signal detection of the time grid sensor. The tunnel magnetoresistance effect sensor (TMR) is adopted to detect the change of the rotor magnetic field of the motor in this method, and the detection model of the time grid sensor about PMSM is constructed. The monostable stochastic resonance theory is applied to extract the induction signal of the time grid sensor. As to the problem of the tuning the parameters of the monostable stochastic resonance system, the genetic algorithm is adopted to optimize the parameters of the monostable stochastic resonance system. The experimental results show that the monostable stochastic resonance method based on the genetic algorithm can effectively detect the weak induction signal of the time grid sensor about PMSM. This method solves the problem of the weak signal extraction of the time grid sensor for PMSM, and the detection accuracy is also improved.

Adaptive monostable stochastic resonance for processing UV absorption spectrum of nitric oxide.

When ultraviolet (UV) absorption spectroscopy technology is used for nitric oxide (NO) detection, the background noise will directly affect the accuracy of concentration inversion, especially in low concentrations. Traditional processing methods attempt to eliminate background noise, which damages the absorption spectrum characteristics. However, stochastic resonance (SR) can utilize the noise to extract a weak characteristic signal. This paper reports a monostable stochastic resonance (MSR) model for processing an UV NO absorption spectrum. By analyzing the characteristics of UV absorption spectrum of NO, the evaluation indexes were constructed, thereby an adaptive MSR method was designed for parameter optimization. The numerical simulation confirmed the absorbance peak can be amplified and spectral signal-to-noise ratio (SNR) can be in the stable range of the proposed method, when noise intensity increased. Finally, this experiment obtained a NO detection limit (3σ) of 1.456 ppm and the maximum relative deviation of concentration is 6.32% by this proposed method, which is satisfactory for processing of the UV NO absorption spectrum.

Stochastic resonance in a monostable system driven by time-delayed feedback

The characteristic of a monostable stochastic resonance system driven by time-delayed feedback is investigated. Under the small-delay approximation theory, the effective potential function of the system is obtained and the influence of system parameters on the shape of the potential function is also discussed. Furthermore, we consider the influence of the input signal on the system and derive the asymmetric bistable potential function. By using the adiabatic approximation theory and the two-state theory, the theoretical expressions of the steady-state probability distribution function, mean first-passage time and signal-to-noise ratio are obtained, which are three excellent metrics to measure the performance of system. Simulation results show that the parameters A, a and τ can motivate the SR phenomenon while β suppresses the SR phenomenon. At last, the numerical simulation results obtained from the original Langevin equation and the effective Langevin equation can verify whether the theoretical derivation is correct.

Rolling bearing fault diagnosis based on time-delayed feedback monostable stochastic resonance and adaptive minimum entropy deconvolution

Rolling bearings are the key components in the modern machinery, and tough operation environments often make them prone to failure. However, due to the influence of the transmission path and background noise, the useful feature information relevant to the bearing fault contained in the vibration signals is weak, which makes it difficult to identify the fault symptom of rolling bearings in time. Therefore, the paper proposes a novel weak signal detection method based on time-delayed feedback monostable stochastic resonance (TFMSR) system and adaptive minimum entropy deconvolution (MED) to realize the fault diagnosis of rolling bearings. The MED method is employed to preprocess the vibration signals, which can deconvolve the effect of transmission path and clarify the defect-induced impulses. And a modified power spectrum kurtosis (MPSK) index is constructed to realize the adaptive selection of filter length in the MED algorithm. By introducing the time-delayed feedback item in to an over-damped monostable system, the TFMSR method can effectively utilize the historical information of input signal to enhance the periodicity of SR output, which is beneficial to the detection of periodic signal. Furthermore, the influence of time delay and feedback intensity on the SR phenomenon is analyzed, and by selecting appropriate time delay, feedback intensity and re-scaling ratio with genetic algorithm, the SR can be produced to realize the resonance detection of weak signal. The combination of the adaptive MED (AMED) method and TFMSR method is conducive to extracting the feature information from strong background noise and realizing the fault diagnosis of rolling bearings. Finally, some experiments and engineering application are performed to evaluate the effectiveness of the proposed AMED-TFMSR method in comparison with a traditional bistable SR method.

Weak thruster fault detection for AUV based on stochastic resonance and wavelet reconstruction

When the bi-stable stochastic resonance method was applied to enhance weak thruster fault for autonomous underwater vehicle (AUV), the enhancement performance could not satisfy the detection requirement of weak thruster fault. As for this problem, a fault feature enhancement method based on mono-stable stochastic resonance was proposed. In the method, in order to improve the enhancement performance of weak thruster fault feature, the conventional bi-stable potential function was changed to mono-stable potential function which was more suitable for aperiodic signals. Furthermore, when particle swarm optimization was adopted to adjust the parameters of mono-stable stochastic resonance system, the global convergent time would be long. An improved particle swarm optimization method was developed by changing the linear inertial weighted function as nonlinear function with cosine function, so as to reduce the global convergent time. In addition, when the conventional wavelet reconstruction method was adopted to detect the weak thruster fault, undetected fault or false alarm may occur. In order to successfully detect the weak thruster fault, a weak thruster detection method was proposed based on the integration of stochastic resonance and wavelet reconstruction. In the method, the optimal reconstruction scale was determined by comparing wavelet entropies corresponding to each decomposition scale. Finally, pool-experiments were performed on AUV with thruster fault. The effectiveness of the proposed mono-stable stochastic resonance method in enhancing fault feature and reducing the global convergent time was demonstrated in comparison with particle swarm optimization based bi-stochastic resonance method. Furthermore, the effectiveness of the proposed fault detection method was illustrated in comparison with the conventional wavelet reconstruction.

Spectrum Sensing Based on Monostable Stochastic Resonance in Cognitive Radio Networks

The cognitive radio technology can provide dynamic spectrum access and improve the efficiency of spectrum utilization. Spectrum sensing is one of the key technologies of cognitive radio networks. The spectrum sensing performance of cognitive radio networks will be greatly reduced in the low SNR environment, especially when using energy detection. Due to the monostable stochastic resonance system can improve the energy detection system output SNR, a monostable stochastic resonanceis applied to spectrum sensing based on the energy detection method of cognitive radio networks in this paper. The simulation results show that in the low SNR environment, when the false alarm probability is constant, the proposed spectrum sensing based on monostable stochastic resonance has better performance than traditional energy detection.

Characteristic analysis of power function type monostable stochastic resonance with Levy noise

In this paper, the Levy noise is combined with a power function type monostable stochastic resonance system for the first time. In order to ensure the reliability of the experimental data, the average signal-to-noise ratio gain is regarded as an index to investigate the stochastic resonance phenomenon stimulated by Levy noise. Potential function form of the monostable system and the method of generating Levy noise are presented in detail. The pulse characteristic and smear characteristic of Levy noise are also presented in detail. The laws for the resonant output of monostable system, governed by parameters a and b, the intensity amplification factor D of Levy noise, are explored under different values of characteristic index and symmetry parameter of Levy noise. Results show that no matter whether it is under any different characteristic index or symmetry parameter of Levy noise, the weak signal can be detected by adjusting the system parameters a and b. The intervals of a and b which can induce stochastic resonances are multiple, and do not change with nor . Moreover, the same rule is founded which by adjusting the intensity amplification factor D of Levy noise can also realize synergistic effect when studying the noise-induced stochastic resonance, and the interval of D does not change with nor ; the best value of characteristic index is =1 under any system parameter, and the best value of symmetry parameter is =1 under any system parameter. So, the system performance is best when =1 and =1. Finally, the interaction relationship between system parameters a and b is investigated, and it is found that the interval of a or b will change with b or a when characteristic index , symmetry parameter and the intensity amplification factor D of Levy noise are fixed. These results will contribute to reasonably choosing the system parameters and intensity amplification factor of power function type monostable stochastic resonance system under Levy noise, and provide a reliable basis for practical engineering application of weak signal detection by stochastic resonance.

Pulse response of a monostable system

The potential function of a mono-stable system is studied in this paper. The response of pulse series with different half-peak width via the mono-stable system is analysed. Our conclusion is that the larger the half-peak width of the input pulse series, the higher the height of the output pulse series . Distortion of the pulse response wave appears. This is the reason that the potential function of the mono-stable system is similar to the horizontal line around zero point.#br#In view of the difficulties of adjusting parameter of the mono-stable system to reach stochastic resonance, a method of moving pulse series is put forward. Adjusting the system parameter is not considered but the stochastic resonance of the pulse signal is realized by setting an offset in the method. To reduce the response pulse wave distortion, a mechanism for the proposed method to reduce the distortion is discussed in detail. When noise exists, the mechanism reveals that the moving pulse series method can adjust the distribution of the noise power spectrum and improve the mono-stable stochastic resonance. Therefore, the method proposed in this paper is helpful to detect pulse signal masked by noise.

Stochastic resonance in an overdamped monostable system with multiplicative and additive α stable noise

In this paper we combine α stable noise with a monostable stochastic resonance (SR) system to investigate the overdamped monostable SR phenomenon with multiplicative and additive α stable noise, and explore the action laws of the stability index α (0 α ≤ 2) and skewness parameter β (-1 ≤ β ≤ 1) of the α stable noise, the monostable system parameter a, and the amplification factor D of the multiplicative α stable noise against the resonance output effect. Results show that for different distributions of α stable noise, the single or multiple low-and high-frequency weak signals detection can be realized by adjusting the parameter a or D within a certain range. For a or D, respectively, there is an optimal value which can make the system produce the best SR effect. Different α or β can regularly change the system resonance output effect. Moreover, when α or β is given different values, the evolution laws in the monostable SR system excited by low-and high-frequency weak signals are the same. The conclusions drawn for the study of single-and multi-frequency monostable SR with α stable noise are also the same. These results will be the foundation for realizing the adaptive parameter adjustment in the monostable SR system with α stable noise.

Virtual Instrument for Weak Signal Detecting on Monostable Stochastic Resonance

Stochastic resonance (SR) is a nonlinear phenomenon which can be used to detect weak signal. The theory of SR in a biased mono-stable system driven by multiplicative and additive white noise as well as a weak periodic signal is investigated. The virtual instrument (VI) for weak signal detecting based on this theory is designed with LabVIEW. This instrument can be used to detect weak periodic signals which meets the conditions given and can greatly improved the power spectrum of the weak signal. The results that related to different sets of parameters are given and the features of these results are in accordance with the theory of mono-stable SR. Thus, the application of this theory in the detecting of weak signal is proven to be valid.

Numerical research of signal-to-noise ratio gain on a monostable stochastic resonance

We report a stochastic resonance with the signal-to-noise ratio gain in a monostable system, by the fourth-order Runge-Kutta method, and on some occasions the signal-to-noise ratio gain exceeds 1. Tuning the parameters in the monostable stochastic resonance system can change the signal-to-noise ratio gain. This research result is the latest development of the monostable stochastic resonance, and has potential applications in the signal detection, processing and communications.

Adaptive Monostable Stochastic Resonance Based on PSO with Application in Impact Signal Detection

Based on the characteristics of the resonance in single potential well of impact signal and the reasonable selection of parameters lacking of effective theoretical basis and the deficiency of single parameter optimization in traditional adaptive stochastic resonance,a new adaptive monostable stochastic resonance based on particle swarm optimization(PSO),which can realize multi-parameter synchronous optimization,is proposed.The model of monostable stochastic resonance that avoids the resonance transition between potential wells in classical bistable system is applied and the weighted kurtosis index of the output of the monostable system is determined as the fitness function of PSO algorithm and multi-parameter in stochastic resonance are selected adaptively.As a result,the impact components in original signals are detected effectively.The algorithm procedure of the impact with adaptive stochastic resonance,combining PSO with the scale transformation stochastic resonance,is provided.The proposed method is applied to the simulation of impact signal and the detection of engineering impact signal,and the results show that the presented method can raise the signal-to-noise ratio effectively,which has advantages of simplicity and fast convergence speed,and possesses a good prospect of engineering application.

Application of Stochastic Resonance Signal Recovery

Stochastic resonance(SR) enhances the nonlinear system behavior with the assistance of noise,including the sensitivity and selectivity of the response to the exterior stimulus. The energy-transfer mechanism makes the weak information revealed in the output spectrum,while the time-waveform is distorted. The distortion analysis was made both from the particle's dynamics and signal processing. The factors causing the deviation in the output are presented and the function of the recovery system is proposed. By the investigation of the particle's motion track in the bistable system and the suggested recovery system,the influences of noise and system parameters on the recovery course were discussed. Moreover,the pulse distortion appearing the recovery waveform caused by the particle's transitions at the bistable potential' inflexions was explained. Due to different characteristics,cascaded-bistable SR or mono-stable SR was introduced to process different types of signals. The final recovery signal is just the suggested recovery system's response to the SR output. Meanwhile,the recovery system is optional,as parameter-tuned or parameter-fixed. Since the method requires no average processing,it is applicable to a single sample with limited length. The numerical simulations reveal that the SR recovery method can recover the waveform containing weak information submerged in noise effectively. The engineering application to the vibration analysis of metal cutting chose the combination of mono-stable SR and the parameter-fixed recovery system. Because the optimal SR state is not required strongly,the system parameters are tuned in a wider range than the traditional SR processing methods.

Reply to “Comment on ‘Monostable array-enhanced stochastic resonance’ ”

We take this opportunity to clarify issues raised in the preceding Comment by Soskin and McClintock [Phys. Rev. E. 66, 013101 (2002)]. In particular, we provide further details and results to motivate and explicate the methodologies we have employed to investigate stochastic resonance in arrays of monostable elements.